The FIR was registered at the Vasant Kunj police station in southwest Delhi, they said.
"The professor often makes sexually-coloured remarks, open demands for sex and comments on the figure of almost every girl. If a girl objects, he holds a grudge against her," the women students had said in a statement on Thursday.
"There is a financial nexus between the professor and the administration. No instrument has been purchased for years, but still crores of rupees have been spent," it said.
The statement was issued by them after a press meet on the JNU campus.
The Delhi Police said they would be questioning the professor soon.
The JNU professor, however, told PTI, that he was being targeted by the Left-leaning students.
On Friday, a large number of students of the SLS staged a demonstration and demanded the Dean of the school suspend the professor from all official positions and initiate an inquiry.
In a letter to the Dean, the students said, "As you already know an FIR has been filed against the professor and since he is in several positions of power and holding university posts, we ask you to immediately inform the vice-chancellor and university administration to suspend him from all the positions."
Members of the JNU Students Union, representatives of the discarded Gender Sensitisation Committee against Sexual Harassment (GSCASH) and those belonging to the women's collective Pinjra Tod also took part in the protest.
The protesters have announced a march to the administration block demanding the vice-chancellor to intervene.
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